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CYLINDERS – VOLUME AND SURFACE AREA 10.1.2 VOLUME OF A CYLINDER

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CYLINDERS – VOLUME AND SURFACE AREA 10.1.2 VOLUME OF A CYLINDER
CYLINDERS – VOLUME AND SURFACE AREA
10.1.2
VOLUME OF A CYLINDER
The volume of a cylinder is the area of its base multiplied by its height:
V=B·h
Since the base of a cylinder is a circle of area A = r2π, we can write:
V = r2πh
For additional information, see the Math Notes box in Lesson 10.1.2 of the Core Connections,
Course 3 text.
Example 1
Example 2
?
3 ft
4 ft
SODA
Find the volume of the cylinder above.
Use a calculator for the value of π.
Volume = r2πh
= (3)2π (4)
= 36π
= 113.10 ft3
12 cm
The soda can above has a volume of 355 cm3
and a height of 12 cm. What is its diameter?
Use a calculator for the value of π.
Volume = r2πh
355 = r2π (12)
355
= r2
12π
9.42 = r2
radius = 3.07
diameter = 2(3.07) = 6.14 cm
Problems
Find the volume of each cylinder.
1.
r = 5 cm
h = 10 cm
2.
r = 7.5 in.
h = 8.1 in.
3.
diameter = 10 cm
h = 5 cm
4.
base area = 50 cm2
h = 4 cm
5.
r = 17 cm
h = 10 cm
6.
d = 29 cm
h = 13 cm
Parent Guide with Extra Practice
© 2013 CPM Educational Program. All rights reserved.
85
Find the missing part of each cylinder.
7.
If the volume is 5175 ft3 and the height is 23 ft, find the diameter.
8.
If the volume is 26,101.07 inches3 and the radius is 17.23 inches, find the height.
9.
If the circumference is 126 cm and the height is 15 cm, find the volume.
Answers
1.
785.40 cm3
2.
1431.39 in3
3.
392.70 cm3
4.
200 cm3
5.
9079.20 cm3
6.
8586.76 cm3
7.
16.93 ft
8.
28 inches
9.
18,950.58 cm3
SURFACE AREA OF A CYLINDER
The surface area of a cylinder is the sum of the two base areas and the lateral surface area.
The formula for the surface area is:
SA = 2r2π + πdh or SA = 2r2π + 2πrh
where r = radius, d = diameter, and h = height of the cylinder. For additional information, see
the Math Notes box in Lesson 10.1.3 of the Core Connections, Course 3 text.
8 cm
Example 1
15 cm
Find the surface area of the cylinder at right.
Use a calculator for the value of π.
Step 1: Area of the two circular bases
15 cm
2[(8 cm)2π] = 128π cm2
Step 2: Area of the lateral face
rectangle
π(16)15 = 240π cm2
circumference of base = 16π cm
Step 3: Surface area of the cylinder
128π cm2 + 240π cm2
86
= 368π cm2
≈ 1156.11 cm2
15 cm
© 2013 CPM Educational Program. All rights reserved.
lateral face
Core Connections, Course 3
Example 2
Example 3
10 cm
5 ft
10 cm
SA = 2 r2π + 2πrh
If the volume of the tank above is 500π ft3, what
is the surface area?
= 2(5)2 π + 2π · 5 · 10
V = π r 2h
= 50π + 100π
SA = 2r 2π + 2π rh
500π = π r 2 (5)
= 150π ≈ 471.24 cm2
500π
5π
= 2 ⋅10 2 π + 2π (10)(5)
= 200π + 100π
= r2
100 = r 2
10 = r
= 300π ≈ 942.48 ft 2
Problems
Find the surface area of each cylinder.
1.
r = 6 cm, h = 10 cm
2.
r = 3.5 in., h = 25 in.
3.
d = 9 in., h = 8.5 in.
4.
d = 15 cm, h =10 cm
5.
base area = 25,
height = 8
6.
Volume = 1000 cm3,
height = 25 cm
Answers
1.
603.19 cm2
2.
626.75 in.2
3.
367.57 in.2
4.
824.69 cm2
5.
191.80 un.2
6.
640.50 cm2
Parent Guide with Extra Practice
© 2013 CPM Educational Program. All rights reserved.
87
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